Biplanar gradient coil design by simulated annealing

Simulated annealing has been applied to the design of biplanar gradient coils for use in NMR microscopy. This method allows a variety of coil parameters to be considered, such as homogeneity over a specified region of interest (ROI), power dissipation, and efficiency. Chosen parameters are represented in an overall figure of merit which is then minimized by the simulated annealing approach. Unlike most analytical techniques which rely on the use of the stream function, with this technique the coil properties are calculated directly from the wire positions, so there is no stage of approximation between current density and the actual coil design. Using this technique, we have designed biplanar x and z gradient coils for use in an 11.7-T NMR microscope. In each case, the coils were composed of straight wire units. The plane spacing was set at 10 mm and the ROI was a central cube of side 6 mm. Starting from a design generated using the target field approach, simulated annealing was applied with the aim of minimizing the ratio of power dissipation per unit current to the square root of coil efficiency while maintaining adequate gradient homogeneity. The efficiency and power dissipation per unit current of the resulting x and z coils were 117 mT m^–1 A^–1 and 0.1 W A^–2, and 99 mT m^–1 A^–1 and 0.4 W A^–2, respectively.     

Versatile coil design and positioning of transverse-field RF surface coils for clinical 1.5-T MRI applications

Clinical MRI/MRS applications require radio frequency (RF) surface coils positioned at an arbitrary angle with respect to B₀. In these experimental conditions the standard circular loop (CL) coil, producing an axial RF field, shows a large signal loss in the central region of interest (ROI). We demonstrate that transverse-field figure-of-eight (FO8) RF surface coils design are not subject to the same amount of signal loss in the central ROI as loop coils when their orientations are changed. The 1.5-T CL and FO8 prototypes (diameter = 10 cm) were built on Plexiglas using copper strips (width = 4 mm, thickness = 100 m). The two linear elements of the FO8 coil were 1 cm apart. Axial spoiled gradient echo (SPGR) images of a phantom containing doped water were acquired with the coil plane at =0°, 45°, and 90°. As increases, the CL images show, in the central ROI, a signal that decreases from a maximum value to zero. Whereas the FO8 images show, in the same ROI, a signal that varies little from the maximum value (20%). Optimized FO8 coils can be oriented with the coil plane positioned along any direction with respect to B₀ without significant signal loss. Transverse RF coil design should be useful for clinical MRS studies and also for parallel imaging techniques where versatile RF coils disposed along arbitrary directions are required.     

Commissioning of the Iseult CEA 11.7 T whole-body MRI: current status,gradient–magnet interaction tests and first imaging experience

Objectives

The Iseult MRI is an actively shielded whole-body magnet providing a homogeneous and stable magnetic field of 11.7 T. After nearly 20 years of research and development, the magnet successfully reached its target field strength for the first time in 2019. This article reviews its commissioning status, the gradient–magnet interaction test results and first imaging experience.

Materials and methods

Vibration, acoustics, power deposition in the He bath, and field monitoring measurements were carried out. Magnet safety system was tested against outer magnetic perturbations, and calibrated to define a safe operation of the gradient coil. First measurements using parallel transmission were also performed on an ex-vivo brain to mitigate the RF field inhomogeneity effect.

Results

Acoustics measurements show promising results with sound pressure levels slightly above the enforced limits only at certain frequency intervals. Vibrations of the gradient coil revealed a linear trend with the B₀ field only in the worst case. Field monitoring revealed some resonances at some frequencies that are still under investigation.

Discussion

Gradient-magnet interaction tests at up to 11.7 T are concluded. The scanner is now kept permanently at field and the final calibrations are on-going to pave the road towards the first acquisitions on volunteers.

     

Comparison of three commercially available radio frequency coils for human brain imaging at 3 Tesla

Objective To evaluate a transverse electromagnetic (TEM), a circularly polarized (CP) (birdcage), and a 12-channel phased array head coil at the clinical field strength of B ₀ = 3T in terms of signal-to-noise ratio (SNR), signal homogeneity, and maps of the effective flip angle α. Materials and methods SNR measurements were performed on low flip angle gradient echo images. In addition, flip angle maps were generated for α_nominal = 30° using the double angle method. These evaluation steps were performed on phantom and human brain data acquired with each coil. Moreover, the signal intensity variation was computed for phantom data using five different regions of interest. Results In terms of SNR, the TEM coil performs slightly better than the CP coil, but is second to the smaller 12-channel coil for human data. As expected, both the TEM and the CP coils show superior image intensity homogeneity than the 12-channel coil, and achieve larger mean effective flip angles than the combination of body and 12-channel coil with reduced radio frequency power deposition. Conclusion At 3T the benefits of TEM coil design over conventional lumped element(s) coil design start to emerge, though the phased array coil retains an advantage with respect to SNR performance.     

High-resolution imaging at 3T and 7T with multiring local volume coils

Magnetic resonance (MR) microimaging of the human is becoming increasingly common for studies of tissue microstructure and microfunction. In this study, we consider the constraints that such experiments place on the design of radio-frequency (rf) coils, and describe the advantages of multiring coils, which offer a locally uniform B₁ field. We show that these coils are particularly suitable for high-field imaging of a restricted region of larger experimental animals or humans, offering the same simplicity and efficient use of rf power as a simple surface coil but without requiring sequence modifications such as adiabatic pulses. Imaging results are shown from human brain and from the abdominal aorta of an experimental animal.Acknowledgements. We thank Dr. S. King for his helpful assistance.     

The modular (twin) gradient coil—high resolution, high contrast, diffusion weighted EPI at 1.0 Tesla

The modular (twin) gradient coil is a novel and effective approach to obtaining flexible and high power gradient performance without (i) peripheral nerve stimulation and (ii) the need for resonant or expensive high voltage gradient power supply units (PSU). This whole-body gradient system contains, on the same former, two independent sets of gradient coils, theconventional coil set and theshort-body coil set. Each gradient axis is able to operate, independently, in any one of three modes. The third,combined, mode is realized by connecting theconventional coils andshort-body coils in series. Through careful design of the shape and size of the linear volume of each mode of operation, the modular gradient coil is able to utilize the power, from a single gradient PSU, more efficiently and more appropriately, as determined by the application. In theshort-body andcombined modes the gradient fields are linear over a volume suitable for whole head/neck, liver and cardiovascular applications. In theconventional mode, a reduced performance is possible but over a much larger (conventional) imaging volume. Utilizing a semi-conductor switching arrangement it is possible to switch between modes in as little as 1 ms. By mixing different modes of operation on different gradient axes it is possible to utilize more efficiently, and safely, the properties of gradient performance best suited to the sequence requirements. Diffusion weighted EPI (DW-EPI) is a particular technique that demands the extremes of gradient system performance in terms of both amplitude and slew rate. DW-EPI has been implemented, using the modular gradient system, on a 1.0 Tesla whole-body MRI system. The preliminary results presented here serve to illustrate the advantages of the modular gradient coil in of itself as well as the direct benefits it provides for DW imaging at 1.0 Tesla.     

A Statistical Study of Small Induction Motor Coil Failures

ABSTRACT

The first purpose of this paper is to clarify statistically which factors affect the outage of induction motor coils and which factors do not affect the outage. The second purpose of this paper is to find statistically how to decide design factors to reduce the outage of coils quantitatively. Up to now such result has hardly been reported.

We statistically analyzed 128 outage of coils from 16 kinds of induction motors in the last eight years and tried to obtain a design guideline for induction motor coils. Six design factors were considered. They are (1)protection of induction motor frame, (2)winding method of the coils, (3)temperature rise in the coils, (4)space factor of coils in the stator slot. (5)an index number of coil damage and (6)an index number of stress on the coil ends.

As a result of the analysis of variance for (1)–(4),the difference is not significant, but for (5) and (6) there is a 1% level of significance in its difference. The outage decreases by about 10% as (5) or (6) decreases by 10%. Thus coil outage can be dealt quantitatively in design which has been considered only qualitatively until now. Better optimum design of induction motors can be performed by using these index numbers as design guidelines with characteristic, economical and manufacturing factors.     

A simple method for mapping the B1 field distribution of linear RF coils

Inhomogeneity of the radio frequency (RF) field B₁ leads to intensity variations in MR images and to spatial dependence of spectral line amplitudes. In this paper, a simple method of measuring the B₁ field components of an unsegmented linear coil is described. The method is designed for the coils operating up to 20 MHz. The B₁ field distribution is replaced by the static magnetic field caused by DC current flowing through the coil. The technique involves rotating the coil 90° so that measured B₁ component is aligned with B₀ and measuring the shift of resonance frequency using a spectroscopic imaging sequence. Experimental results were in good agreement with the theoretical computations.     

B1 field-insensitive transformers for RF-safe transmission lines

Objective: Integration of transformers into transmission lines suppresses radiofrequency (RF)-induced heating. New figure-of-eight-shaped transformer coils are compared to conventional loop transformer coils to assess their signal transmission properties and safety profile. Materials and methods: The transmission properties of figure-of-eight-shaped transformers were measured and compared to transformers with loop coils. Experiments to quantify the effect of decoupling from the B₁ field of the MR system were conducted. Temperature measurements were performed to demonstrate the effective reduction of RF-induced heating. The transformers were investigated during active tracking experiments. Results: Coupling to the B₁ field was reduced by 18 dB over conventional loop-shaped transformer coils. MR images showed a significantly reduced artifact for the figure-of-eight- shaped coils generated by local flip-angle amplification. Comparable transmission properties were seen for both transformer types. Temperature measurements showed a maximal temperature increase of 30K/3.5 K for an unsegmented/ segmented cable. With a segmented transmission line a robotic assistance system could be successfully localized using active tracking. Conclusion: The figure-of-eight-shaped transformer design reduces both RF field coupling with the MR system and artifact sizes. Anatomical structure close to the figure-of-eight-shaped transformer may be less obscured as with loop-shaped transformers if these transformers are integrated into e.g. intravascular catheters.     

Simulation-based evaluation of SAR and flip angle homogeneity for five transmit head arrays at 14 T

Introduction

Various research sites are pursuing 14 T MRI systems. However, both local SAR and RF transmit field inhomogeneity will increase. The aim of this simulation study is to investigate the trade-offs between peak local SAR and flip angle uniformity for five transmit coil array designs at 14 T in comparison to 7 T.

Methods

Investigated coil array designs are: 8 dipole antennas (8D), 16 dipole antennas (16D), 8 loop coils (8D), 16 loop coils (16L), 8 dipoles/8 loop coils (8D8L) and for reference 8 dipoles at 7 T. Both RF shimming and k_T-points were investigated by plotting L-curves of peak SAR levels vs flip angle homogeneity.

Results

For RF shimming, the 16L array performs best. For k_T-points, superior flip angle homogeneity is achieved at the expense of more power deposition, and the dipole arrays outperform the loop coil arrays.

Discussion and conclusion

For most arrays and regular imaging, the constraint on head SAR is reached before constraints on peak local SAR are violated. Furthermore, the different drive vectors in k_T-points alleviate strong peaks in local SAR. Flip angle inhomogeneity can be alleviated by k_T-points at the expense of larger power deposition. For k_T-points, the dipole arrays seem to outperform loop coil arrays.

     

高压电子电流互感器Rogowski线圈优化设计

根据安培环路定律和法拉第电磁感应定律,导出了有源型高压电子电流互感器传感头重要组成部分的Rogowski线圈感应电压数学模型。通过建立装配间隙系数、线圈等效尺寸等概念,讨论了决定线圈互感值大小的各项结构参数,得到了依据互感梯度物理意义而提出的Rogowski线圈最优结构设计参数计算模型,即有约束非线性最优化问题。给出了Rogowski线圈结构设计的应用实例,在MATLAB上的计算仿真结果与实际情况相符合,为有源型高压电子电流互感器Rogowski线圈结构优化设计提供了一种理论依据。     

Performance evaluation of matrix gradient coils

Objective

In this paper, we present a new performance measure of a matrix coil (also known as multi-coil) from the perspective of efficient, local, non-linear encoding without explicitly considering target encoding fields.

Materials and methods

An optimization problem based on a joint optimization for the non-linear encoding fields is formulated. Based on the derived objective function, a figure of merit of a matrix coil is defined, which is a generalization of a previously known resistive figure of merit for traditional gradient coils.

Results

A cylindrical matrix coil design with a high number of elements is used to illustrate the proposed performance measure. The results are analyzed to reveal novel features of matrix coil designs, which allowed us to optimize coil parameters, such as number of coil elements. A comparison to a scaled, existing multi-coil is also provided to demonstrate the use of the proposed performance parameter.

Conclusions

The assessment of a matrix gradient coil profits from using a single performance parameter that takes the local encoding performance of the coil into account in relation to the dissipated power.

     

3D gradient system for two B 0 field directions in earth’s field MRI

Object

A new gradient system for earth’s field magnetic resonance imaging (EFMRI) is presented that can be rotated relatively to the earth’s field direction while maintaining the ability to encode images. Orthogonal components of the gradient field are exploited to reduce the number of gradient coils.

Materials and methods

Two favorable orientations of the gradient system relative to the earth’s magnetic field (parallel and perpendicular) are discussed. We introduce the theory for the magnetic fields of the new gradient system and illustrate the design of the coil geometries which were worked out with the help of simulations and a numerical optimization algorithm. Field mapping measurements and imaging experiments in the two different orientations of the gradient system were carried out.

Results

Orthogonal components of the gradient field take over the role of the additionally needed gradient fields when the gradient system is rotated relative to the earth’s magnetic field. The results from the field mapping and imaging experiments verify the presented theory and show the functionality of the new gradient system.

Conclusion

The presented system demonstrates that gradient coils can be used for image encoding in multiple directions. This fact can be exploited to realize an EFMRI setup for parallel and perpendicular prepolarization with a single set of gradient coils.     

Electromagnetic characterisation of MR RF coils using the transmission-line modelling method

The Transmission-Line Modelling (TLM) method is applied to the electromagnetic characterisation of RF coils and samples for magnetic resonance imaging ()MRI. Theoretical verification was performed using a simple surface coil. Experimental verification was performed using Alderman-Grant and birdcage coils constructed for use on a 7 T micro-imaging system. The modelling method enabled electromagnetic characteristics of frequency response, electromagnetic field generation, energy stored and power loss to be determined. From these parameters, coil resonant modes.B ₁ field profiles, voltages, currents, quality factor (Q),π/2 pulse length, and the equivalent lumped-element circuit components of resistance, inductance and capacitance were calculated. Equations are presented that enable a comprehensive electromagnetic characterisation of the RF coil and sample to be achieved based on the results of the TLM simulations. The use of the TLM method is extended to include the design of safe arbitrary multi-nuclear pulse sequences such that the specific absorption rate (SAR) of tissue, and RF coil component safety limits are not exceeded.     

Development of a 400 kJ Nb3Sn superconducting magnet for an SMES system

An Nb₃Sn superconducting magnet to store 400 kJ was developed as a unit magnet for a 2.4-MJ SMES system used for stabilization studies of electrical power systems. The superconducting magnet consists of a cryostat and an Nb₃Sn coil. The dimensions of the coil are: 340 mm inner diameter, 700 mm outer diameter and 177 mm axial length. The pool-cooled coil is a stack of 20 Nb₃Sn double pancakes, and the cooling channels are aligned between pancake coils. To reduce Joule loss in electrical power converters, the maximum operating current of the coil is designed to be 350 A, which is one order of magnitude less than the operating currents of similar scale coils for pulse use. The conductor is an Nb₃Sn monolithic conductor with cross section 1.50 × 2.38 mm. For good superconducting stability and high dielectric strength of the coil, the Nb₃Sn double pancakes were wound by the react-and-wind technique. Operation of dc current to 105% (367.5 A) of the design operating current was achieved without quench. After the whole of the coil was exposed out of liquid helium, the coil did not quench under 120 A current operation for more than 2 hours. It was verified that the coil was stable for the SMES system. © 1998 Scripta Technica, Inc. Electr Eng Jpn, 121(3): 44–52, 1997     

An integrated target field framework for point-of-care halbach array low-field MRI system design

Objective

Low-cost low-field point-of-care MRI systems are used in many different applications. System design has correspondingly different requirements in terms of imaging field-of-view, spatial resolution and magnetic field strength. In this work an iterative framework has been created to design a cylindrical Halbach-based magnet along with integrated gradient and RF coils that most efficiently fulfil a set of user-specified imaging requirements.

Methods

For efficient integration, target field methods are used for each of the main hardware components. These have not been used previously in magnet design, and a new mathematical model was derived accordingly. These methods result in a framework which can design an entire low-field MRI system within minutes using standard computing hardware.

Results

Two distinct point-of-care systems are designed using the described framework, one for neuroimaging and the other for extremity imaging. Input parameters are taken from literature and the resulting systems are discussed in detail.

Discussion

The framework allows the designer to optimize the different hardware components with respect to the desired imaging parameters taking into account the interdependencies between these components and thus give insight into the influence of the design choices.

     

Ramping down a clinical 3 T scanner: a journey into MRI and MRS at 0.75 T

Object

Lower-field MR is reemerging as a viable, potentially cost-effective alternative to high-field MR, thanks to advances in hardware, sequence design, and reconstruction over the past decades. Evaluation of lower field strengths, however, is limited by the availability of lower-field systems on the market and their considerable procurement costs. In this work, we demonstrate a low-cost, temporary alternative to purchasing a dedicated lower-field MR system.

Materials and Methods

By ramping down an existing clinical 3 T MRI system to 0.75 T, proton signals can be acquired using repurposed ¹³C transmit/receive hardware and the multi-nuclei spectrometer interface. We describe the ramp-down procedure and necessary software and hardware changes to the system.

Results

Apart from presenting system characterization results, we show in vivo examples of cardiac cine imaging, abdominal two- and three-point Dixon-type water/fat separation, water/fat-separated MR Fingerprinting, and point-resolved spectroscopy. In addition, the ramp-down approach allows unique comparisons of, e.g., gradient fidelity of the same MR system operated at different field strengths using the same receive chain, gradient coils, and amplifiers.

Discussion

Ramping down an existing MR system may be seen as a viable alternative for lower-field MR research in groups that already own multi-nuclei hardware and can also serve as a testing platform for custom-made multi-nuclei transmit/receive coils.

     

Specific absorption rate (SAR) simulations for low-field (< 0.1 T) MRI systems

Objective

To simulate the magnetic and electric fields produced by RF coil geometries commonly used at low field. Based on these simulations, the specific absorption rate (SAR) efficiency can be derived to ensure safe operation even when using short RF pulses and high duty cycles.

Methods

Electromagnetic simulations were performed at four different field strengths between 0.05 and 0.1 T, corresponding to the lower and upper limits of current point-of-care (POC) neuroimaging systems. Transmit magnetic and electric fields, as well as transmit efficiency and SAR efficiency were simulated. The effects of a close-fitting shield on the EM fields were also assessed. SAR calculations were performed as a function of RF pulse length in turbo-spin echo (TSE) sequences.

Results

Simulations of RF coil characteristics and B₁⁺ transmit efficiencies agreed well with corresponding experimentally determined parameters. Overall, the SAR efficiency was, as expected, higher at the lower frequencies studied, and many orders of magnitude greater than at conventional clinical field strengths. The tight-fitting transmit coil results in the highest SAR in the nose and skull, which are not thermally sensitive tissues. The calculated SAR efficiencies showed that only when 180° refocusing pulses of duration ~ 10 ms are used for TSE sequences does SAR need to be carefully considered.

Conclusion

This work presents a comprehensive overview of the transmit and SAR efficiencies for RF coils used for POC MRI neuroimaging. While SAR is not a problem for conventional sequences, the values derived here should be useful for RF intensive sequences such as T_1ρ, and also demonstrate that if very short RF pulses are required then SAR calculations should be performed.

     

Optimized quadrature surface coil designs

Background Quadrature surface MRI/MRS detectors comprised of circular loop and figure-8 or butterfly-shaped coils offer improved signal-to-noise-ratios (SNR) compared to single surface coils, and reduced power and specific absorption rates (SAR) when used for MRI excitation. While the radius of the optimum loop coil for performing MRI at depth d in a sample is known, the optimum geometry for figure-8 and butterfly coils is not. Materials and methods The geometries of figure-8 and square butterfly detector coils that deliver the optimum SNR are determined numerically by the electromagnetic method of moments. Figure-8 and loop detectors are then combined to create SNR-optimized quadrature detectors whose theoretical and experimental SNR performance are compared with a novel quadrature detector comprised of a strip and a loop, and with two overlapped loops optimized for the same depth at 3 T. The quadrature detection efficiency and local SAR during transmission for the three quadrature configurations are analyzed and compared. Results The SNR-optimized figure-8 detector has loop radius r ₈ ~ 0.6d, so r ₈/r ₀ ~ 1.3 in an optimized quadrature detector at 3 T. The optimized butterfly coil has side length ~ d and crossover angle of ≥ 150° at the center. Conclusions These new design rules for figure-8 and butterfly coils optimize their performance as linear and quadrature detectors. This work is supported by NIH grant R01 RR15396.     

带中继谐振器的磁耦合谐振式无线电能传输系统的效率特性分析

探讨了带中继谐振器的磁耦合谐振式无线电能传输MCR-WPT（magnetic coupling resonant-wireless power transfer）系统的传输效率优化问题。通过构建和分析带中继线圈的等效电路模型,引入功率传输性能参数|S_ij|²推导出当中继线圈和接收线圈位置固定时,发射线圈和带中继谐振器之间的最佳耦合系数的闭合形式解,进而确定发射线圈和带中继谐振器之间的最优距离,实现总系统传输效率最大化。通过线圈设计及相关实验,验证了分析结果与实验结果的一致性。研究结果表明,MCR-WPT系统可方便配置最佳耦合系数以实现电能传输效率最大化,为带中继谐振器的WPT系统效率优化提供重要参考。